Question 1Â Â Â 4 Marks

The following data shows the amount of money (in dollars)
spent by a sample of 24 customers at the local fast food
restaurant.

23Â Â Â 14Â Â
Â 32Â Â Â 9Â Â
Â 32Â Â Â 14Â Â
Â 25Â Â Â 8Â Â
Â 4Â Â Â 19Â Â
Â 21Â Â Â 11

17Â Â Â 18Â Â
Â 19Â Â Â 42Â Â
Â 26Â Â Â 21Â Â
Â 17Â Â Â 19Â Â
Â 21Â Â Â 6Â Â
Â 9Â Â Â 18

(a)Â Â Â Construct a stem-and-leaf diagram
using this data. Â Â Â 1 mark

(b)Â Â Â The restaurant believes that the
average spending of customers is usually less than $25. Using your
answer in (a), comment on this statement (Use 20 to 30
words).Â Â Â 1 mark

(c)Â Â Â Recommend and draw the most suitable
graph for this data. (Use 30 to 50 words to answer this
part)Â Â Â 2 marks

Question 2Â Â Â 4 Marks

The following data shows the share prices (in dollars) of BMW
in the month of November 2015.

DateÂ Â Â Prices ($)

23 Nov 2015Â Â Â 98.45

20 Nov 2015Â Â Â 99.17

19 Nov 2015Â Â Â 98.73

18 Nov 2015Â Â Â 97.45

17 Nov 2015Â Â Â 97.26

16 Nov 2015Â Â Â 94.71

13 Nov 2015Â Â Â 94.54

12 Nov 2015Â Â Â 94.46

11 Nov 2015Â Â Â 96.18

10 Nov 2015Â Â Â 95.93

9 Nov 2015Â Â Â 94.96

6 Nov 2015Â Â Â 96.03

5 Nov 2015Â Â Â 92.78

4 Nov 2015Â Â Â 92.45

3 Nov 2015Â Â Â 93.57

(a)Â Â Â Calculate the mean and standard
deviation for this data.Â Â Â 2 marks

(b)Â Â Â Calculate the Minimum, Q1, Median,
Q3 and Maximum values for this data.Â Â Â 2 marks

Question 3Â Â Â 4 Marks

The table below is taken from the Australian Bureau of
Statistics website. It provides data on household use of the
Internet from 2006 to 2013 in Australia.

Â Â Â Â Â Â Households with
Internet access

Â Â Â Year

FrequencyÂ Â Â Â Â
Â 2006â€“07Â Â Â 2007â€“08Â Â
Â 2008â€“09Â Â Â 2010â€“11Â Â
Â 2012â€“13

Â Â Â Â Â
Â '000Â Â Â '000Â Â
Â '000Â Â Â '000Â Â Â '000

Â Â Â Every dayÂ Â
Â 3,321Â Â Â 3,703Â Â
Â 4,281Â Â Â 5,157Â Â Â 5,933

Â Â Â At least weeklyÂ Â
Â 1,561Â Â Â 1,540Â Â
Â 1,382Â Â Â 1,339Â Â Â 1,202

Â Â Â At least monthlyÂ Â
Â 185Â Â Â 176Â Â
Â 132Â Â Â 148Â Â Â 129

Â Â Â At least yearlyÂ Â
Â 21Â Â Â 26Â Â
Â 25Â Â Â 20Â Â Â 23

Â Â Â NeverÂ Â
Â 31Â Â Â 25Â Â
Â 33Â Â Â 39Â Â Â 31

Â Â Â Don't knowÂ Â
Â 19Â Â Â 20Â Â
Â 26Â Â Â 21Â Â Â 26

Â Â Â TotalÂ Â
Â 5,138Â Â Â 5,492Â Â
Â 5,878Â Â Â 6,724Â Â Â 7,343

(a)Â Â Â Find the probability that a randomly
selected households access the Internet in 2010-2011.Â Â
Â 1 mark

(b)Â Â Â In the years of 2006-2007, what is
the probability that a randomly selected households use the
Internet every day?Â Â Â 1 mark

(c)Â Â Â What is the probability that a
randomly selected households access the Internet at least monthly
or at least yearly?Â Â Â 1 mark

(d)Â Â Â What is the probability that a
randomly selected households access the Internet at least on
monthly basis in 2007-2008?Â Â Â 1 mark

Question 4Â Â

(a)Â Â Â Fiberglass manufacturing company
finds 10% defective items in their production output. The
production manager has been instructed to analyse and recommend
solutions for improving the process. If a sample of 20 items is
inspected, what is the probability of finding exactly two or three
defectives?Â Â Â 1 mark

(b)Â Â Â An emergency unit at the local
hospital has admitted an average of 20 patients per hour. What is
the probability that the next patient will be admitted at least 5
minutes from now?Â Â Â 1 mark

(c)Â Â Â It is observed that the average
share prices of ANZ Bank are normally distributed with a mean of
$27 and a standard deviation of $2.

(i) What proportion of the share prices is between $25 and
$35?Â Â Â 1 mark

(ii) What value do the upper 5% of the share prices exceed?
Â Â Â 1 mark

Question 5Â Â Â 4 Marks

(a)Â Â Â An operator for a
telephone-answering service answers a large number of calls for two
real estate agents. The two agents are charged the same monthly fee
for this service and it is assumed that they will each receive
approximately half the calls coming in. Based on this assumption,
find the probability that in the next 150 calls 90 or more will be
for one agent. (Use normal approximation of the binomial
distribution.)Â Â Â 1 mark

(b)Â Â Â A recent survey conducted by a
Fitness Society found that 60% of Australians who exercise daily by
walking are women. If a random sample is taken of 15 people who
exercise daily, what is the approximate probability that there will
be an exactly 11 females in the group?Â Â Â 1.5
marks

(c)Â Â Â A study on online shopping habits
found that men spend a mean of $2,401, whereas women spend a mean
of $1,527. Suppose that the study was based on a sample of 600 men
and 700 females, and the standard deviation of the amount spent was
$1,200 for men and $1,000 for women.

At the 0.01 level of significance, is there evidence that the
mean amount spent is higher for men than for women?

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